Related papers: Simpler Sequential and Parallel Biconnectivity Aug…
Algorithms for finding minimum or bounded vertex covers in graphs use a branch-and-reduce strategy, which involves exploring a highly imbalanced search tree. Prior GPU solutions assign different thread blocks to different sub-trees, while…
A vertex set $U \subseteq V$ of an undirected graph $G=(V,E)$ is a $\textit{resolving set}$ for $G$, if for every two distinct vertices $u,v \in V$ there is a vertex $w \in U$ such that the distances between $u$ and $w$ and the distance…
Connectivity queries, which check whether vertices belong to the same connected component, are fundamental in graph computations. Sliding window connectivity processes these queries over sliding windows, facilitating real-time streaming…
Graph augmentation is a fundamental and well-studied problem that arises in network optimization. We consider a new variant of this model motivated by reconfigurable communication networks. In this variant, we consider a given physical…
For a graph $G$, $k(G)$ denotes its connectivity. A graph is super connected if every minimum vertex-cut isolates a vertex. Also $k_{1}$-connectivity of a connected graph is the minimum number of vertices whose deletion gives a disconnected…
We consider the ``minimum degree spanning tree'' problem. As input, we receive an undirected, connected graph $G=(V, E)$ with $n$ nodes and $m$ edges, and our task is to find a spanning tree $T$ of $G$ that minimizes $\max_{u \in V}…
The optimal connecting network problem generalizes many models of structure optimization known from the literature, including communication and transport network topology design, graph cut and graph clustering, structure identification from…
A linked bar chart is the augmentation of a traditional bar chart where each bar is partitioned into blocks and pairs of blocks are linked using orthogonal lines that pass over intermediate bars. The order of the blocks readily influences…
Given a set $P$ of terminals in the plane and a partition of $P$ into $k$ subsets $P_1, ..., P_k$, a two-level rectilinear Steiner tree consists of a rectilinear Steiner tree $T_i$ connecting the terminals in each set $P_i$ ($i=1,...,k$)…
This paper makes two main contributions: The first is the construction of a near-minimum spanning tree with constant average distortion. The second is a general equivalence theorem relating two refined notions of distortion: scaling…
Data augmentation is widely used for training a neural network given little labeled data. A common practice of augmentation training is applying a composition of multiple transformations sequentially to the data. Existing augmentation…
Connectivity and diagnosability are two important parameters for the fault tolerant of an interconnection network $G$. In 1996, F\`{a}brega and Fiol proposed the $g$-extra connectivity of $G$. A subset of vertices $S$ is said to be a…
Let $G$ be a connected graph. The edge-connectivity of $G$, denoted by $\lambda(G)$, is the minimum number of edges whose removal renders $G$ disconnected. Let $\delta(G)$ be the minimum degree of $G$. It is well-known that $\lambda(G) \leq…
We study dynamic planar graphs with $n$ vertices, subject to edge deletion, edge contraction, edge insertion across a face, and the splitting of a vertex in specified corners. We dynamically maintain a combinatorial embedding of such a…
An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V, E) and the goal is to find a subset of vertices S $\subseteq$ V that maximizes the number of edges in the cut \delta(S) such that the induced graph…
Augmenting an existing sequential data structure with extra information to support greater functionality is a widely used technique. For example, search trees are augmented to build sequential data structures like order-statistic trees,…
We investigate the structure of trees that have minimal algebraic connectivity among all trees with a given degree sequence. We show that such trees are caterpillars and that the vertex degrees are non-decreasing on every path on…
The wavelet tree (Grossi et al. [SODA, 2003]) and wavelet matrix (Claude et al. [Inf. Syst., 47:15--32, 2015]) are compact indices for texts over an alphabet $[0,\sigma)$ that support rank, select and access queries in $O(\lg \sigma)$ time.…
We give an $\tilde{O}(m)$-time algorithm for the edge connectivity augmentation problem and the closely related edge splitting-off problem. This is optimal up to lower order terms and closes the long line of work on these problems.
For a graph $G=(V,E)$ and a set $S\subseteq V(G)$ of size at least $2$, an $S$-Steiner tree $T$ is a subgraph of $G$ that is a tree with $S\subseteq V(T)$. Two $S$-Steiner trees $T$ and $T'$ are internally disjoint (resp. edge-disjoint) if…